Finite Group Databasebeta

← #49130805

Subgroups — #49130805

Order 36224.

504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583636C211yesmaximal, characteristic, complemented
2C2×#22583632C211yesmaximal, characteristic, complemented
3#31827032C211yesmaximal, characteristic, complemented
4#31826946C211yesmaximal, characteristic, complemented
5#31826686C212yesmaximal, complemented
6#31826679C212yesmaximal, complemented
7#31826664C212yesmaximal, complemented
8#31826659C212yesmaximal, complemented
9#31826491C211yesmaximal, characteristic, complemented
10#31826464C211yesmaximal, characteristic, complemented
11C2×#102×C283C211yesmaximal, characteristic, complemented
12C2×#17985392C2211yescharacteristic
13C2×#17985392C2211yescharacteristic
14#22583636—24no—
15#22583632—24no—
16C2×Dic1132C2211yescharacteristic, complemented
17C2×#17985381C2211yescharacteristic, complemented
18C2×#17985381C2211yescharacteristic, complemented
19C2×#17985380C2212yes—
20C2×D2264C2211yescharacteristic, complemented
21C2×#17985377C2212yes—
22C2×#17985376C2211yescharacteristic
23#22583606C2212yes—
24#22583597C2212yes—
25#22583581—21no—
26#22583581—21no—
27#22583579—22no—
28#22583575C2212yescomplemented
29#22583572C2212yescomplemented
30C4×C22⋊D283—22no—
31#22583569C2211yescharacteristic
32#22583568—21no—
33C4⋊C4×D283—21no—
34Dic283⋊C8C2212yescomplemented
35Dic283⋊C8C2212yescomplemented
36#22583533C2212yescomplemented
37#22583530C2212yescomplemented
38C22×D4×C283C2211yescharacteristic
39C22×C8×C283C2211yescharacteristic
40C2×C4⋊C4×C283C2211yescharacteristic
41#102×C283C2212yes—
42#102×C283C2212yes—
43#17985392—22no—
44#17985392—22no—
45#17985392—22no—
46#17985392D414yescomplemented
47C2×Dic566C2311yescharacteristic
48C2×Dic566C2311yescharacteristic
49C2×D1132C2311yescharacteristic
50C2×D1132C2311yescharacteristic
51C2×C22⋊D283—22no—
52C2×C22⋊D283—22no—
53C2×C22⋊D283—21no—
54C2×C22⋊D283—21no—
55C2×C4×D283—22no—
56C2×C4×D283—21no—
57C2×C4×D283—21no—
58Dic1132—22no—
59#17985381—22no—
60#17985381—22no—
61#17985380—24no—
62D2264—22no—
63#17985377—24no—
64#17985376—22no—
65C2×C283⋊C8C2312yes—
66C4⋊Dic283D411yescharacteristic
67C4⋊Dic283D411yescharacteristic
68Dic283⋊C4—22no—
69C22⋊Dic283—22no—
70C22⋊Dic283—22no—
71C22⋊Dic283D412yes—
72(C2×D283)⋊C4—22no—
73C4×Dic283—22no—
74C4×Dic283C2312yes—
75C24×C283—21no—
76C2×D4×C283—22no—
77C2×D4×C283—21no—
78C2×D4×C283—22no—
79C2×D4×C283C2312yes—
80C22×C4×C283—21no—
81C22×C4×C283C2311yescharacteristic
82C2×C8×C283—22no—
83C2×C8×C283C2311yescharacteristic
84C2×C8×C283C2311yescharacteristic
85C4⋊C4×C283—21no—
86C4⋊C4×C283C2312yes—
87C22×D283—21no—
88C22×D283—21no—
89Dic566—21no—
90Dic566—21no—
91Dic566—21no—
92Dic566C2×D412yes—
93D1132—21no—
94D1132—21no—
95D1132—21no—
96D1132C2×D412yes—
97C22⋊D283—24no—
98C22⋊D283—42no—
99C22⋊D283—82no—
100C22⋊D283—82no—
101C2×Dic283—21no—
102C2×Dic283—21no—
103C2×Dic283C2×D412yes—
104C2×Dic283C2×D412yes—
105C4×D283—24no—
106C4×D283—42no—
107C4×D283—82no—
108C283⋊C8—22no—
109C23×C283—22no—
110C23×C283—42no—
111C23×C283—81no—
112C23×C283—81no—
113C23×C283C2×D411yescharacteristic
114D4×C283—22no—
115D4×C283—22no—
116D4×C283—42no—
117C2×C4×C283—22no—
118C2×C4×C283—81no—
119C2×C4×C283C2×D411yescharacteristic
120C2×C4×C283C2×D412yes—
121C2×C4×C283#4112yes—
122C2×C4×C283C2411yescharacteristic
123C8×C283—21no—
124C8×C283—21no—
125C22×C283—21no—
126C22×C283—21no—
127C22×C283—42no—
128C22×C283—42no—
129C22×C283—42no—
130C22×C283—84no—
131C22×C283#12112yes—
132C22×C283C22×D411yescharacteristic
133C2×D283—22no—
134C2×D283—41no—
135C2×D283—41no—
136C2×D283—41no—
137C2×D283—41no—
138C2×D283—41no—
139C4×C283—42no—
140C4×C283#12112yes—
141C4×C283C22×D411yescharacteristic
142C4×C283C2×#4111yescharacteristic
143Dic283—22no—
144Dic283—22no—
145Dic283—22no—
146Dic283—41no—
147C2×C283—22no—
148C2×C283—82no—
149C2×C283C2×#12111yescharacteristic
150C2×C283#57611yescharacteristic
151C2×C283#57711yescharacteristic
152D283—42no—
153D283—81no—
154C283#304511yescharacteristic, complemented, Sylow
155#3045—2831nomaximal, Sylow
156C2×AGL(1,ℤ/8)—2831no—
157C2×#135—2831no—
158#535—2831no—
159#520—2831no—
160#464—2832no—
161#463—2832no—
162#460—2832no—
163#459—2832no—
164#424—2831no—
165#417—2831no—
166C2×#102D28311yescharacteristic, complemented
167C2×#41—2831no—
168C2×#41—2831no—
169C22×D4C2×D28311yescharacteristic
170AGL(1,ℤ/8)—5664no—
171#135—5664no—
172C2×Q16—2831no—
173C2×SD16—2832no—
174C2×SD16—2831no—
175C2×SD16—2831no—
176C2×D8—2832no—
177C2×D8—2831no—
178C2×M16—2831no—
179C22×C8C2×D28311yescharacteristic
180#127—2832no—
181#124—2832no—
182#121—5661no—
183#121—5661no—
184#120—5662no—
185C4×Q8—2832no—
186C4×D4—2832no—
187C4×D4—5662no—
188#117—2831no—
189#117—5661no—
190C2×C4⋊C4—5661no—
191C2×C4⋊C4C2×D28311yescharacteristic
192C4⋊C8—2832no—
193C4⋊C8—2832no—
194#103—2832no—
195#102—2832no—
196#102C2×D28312yes—
197#102C2×D28312yes—
198C24—21no—
199#41—2834no—
200#41—5662no—
201#41—5662no—
202#41—5662no—
203C2×Q8—2831no—
204C2×Q8—2831no—
205C2×D4—22no—
206C2×D4—21no—
207C2×D4—22no—
208C2×D4—2831no—
209C2×D4—2831no—
210C2×D4—5662no—
211C2×D4—5662no—
212C2×D4—5661no—
213C2×D4—5661no—
214C2×D4C22×D28312yes—
215C22×C4—21no—
216C22×C4—5662no—
217C22×C4—5661no—
218C22×C4—5661no—
219C22×C4C22×D28311yescharacteristic
220Q16—5662no—
221SD16—5662no—
222SD16—5662no—
223SD16—5664no—
224D8—5662no—
225D8—5664no—
226M16—5662no—
227C2×C8—22no—
228C2×C8—2832no—
229C2×C8C22×D28311yescharacteristic
230C2×C8C22×D28311yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—2831no—
233C4⋊C4—2831no—
234C4⋊C4—5662no—
235C4⋊C4C22×D28312yes—
236C22⋊C4—2832no—
237C22⋊C4—5662no—
238C22⋊C4—5662no—
239C22⋊C4—5662no—
240C42—2832no—
241C42—5662no—
242C23—22no—
243C23—42no—
244C23—81no—
245C23—81no—
246C23—5661no—
247C23—5661no—
248C23D4×D28311yescharacteristic
249Q8—2832no—
250Q8—5661no—
251Q8—5661no—
252Q8—5661no—
253D4—22no—
254D4—22no—
255D4—42no—
256D4—2832no—
257D4—5664no—
258D4—5661no—
259D4—5661no—
260D4—5661no—
261D4—11322no—
262D4—22642no—
263D4—22642no—
264C2×C4—22no—
265C2×C4—81no—
266C2×C4—2832no—
267C2×C4—2832no—
268C2×C4—5661no—
269C2×C4—5664no—
270C2×C4—5661no—
271C2×C4—11322no—
272C2×C4—22642no—
273C2×C4D4×D28311yescharacteristic
274C2×C4D4×D28312yes—
275C2×C4#1798539212yes—
276C2×C4C23×D28311yescharacteristic
277C8—21no—
278C8—21no—
279C8—5662no—
280C22—21no—
281C22—21no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—84no—
286C22—5662no—
287C22—11321no—
288C22—11321no—
289C22—11321no—
290C22—11321no—
291C22—11321no—
292C22#2258358312yes—
293C22C2×D4×D28311yescharacteristic
294C4—42no—
295C4—5662no—
296C4—5662no—
297C4—5662no—
298C4—11321no—
299C4#2258358312yes—
300C4C2×D4×D28311yescharacteristic
301C4C2×#1798539211yescharacteristic
302C2—22no—
303C2—82no—
304C2—11322no—
305C2—22641no—
306C2C2×#2258358311yescharacteristic
307C2#3182726611yescharacteristic
308C2#3182727111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#102×C283C2
socleC22×C283C22×D4
hypercenterC2×#102D283
hypocenterC283#3045
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#22583636C2semidirect
2. C2×#22583632C2semidirect
3. #31827032C2semidirect
4. #31826946C2semidirect
5. #31826686C2semidirect
6. #31826679C2semidirect
7. #31826664C2semidirect
8. #31826659C2semidirect
9. #31826491C2semidirect
10. #31826464C2semidirect
11. C2×#102×C283C2semidirect
16. C2×Dic1132C22semidirect
17. C2×#17985381C22semidirect
18. C2×#17985381C22semidirect
20. C2×D2264C22semidirect
28. #22583575C22semidirect
29. #22583572C22semidirect
34. Dic283⋊C8C22semidirect
35. Dic283⋊C8C22semidirect
36. #22583533C22semidirect
37. #22583530C22semidirect
46. #17985392D4semidirect
154. C283#3045semidirect
166. C2×#102D283semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#225836362
C2×#225836322
#318270322
#318269462
#318266862
#318266792
#318266642
#318266592
#318264912
#318264642
C2×#102×C2832
#3045283